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SageMath
E = EllipticCurve("i1")
E.isogeny_class()
Elliptic curves in class 141120.i
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
141120.i1 | 141120nb2 | \([0, 0, 0, -917868, 367372208]\) | \(-77626969/8000\) | \(-8813365017182208000\) | \([]\) | \(2903040\) | \(2.3747\) | |
141120.i2 | 141120nb1 | \([0, 0, 0, 69972, -499408]\) | \(34391/20\) | \(-22033412542955520\) | \([]\) | \(967680\) | \(1.8254\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 141120.i have rank \(0\).
Complex multiplication
The elliptic curves in class 141120.i do not have complex multiplication.Modular form 141120.2.a.i
sage: E.q_eigenform(10)
Isogeny matrix
sage: E.isogeny_class().matrix()
The \(i,j\) entry is the smallest degree of a cyclic isogeny between the \(i\)-th and \(j\)-th curve in the isogeny class, in the LMFDB numbering.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.